On March 14, 2017 we launched our new project to test the validity of the Collatz conjecture for Mersenne primes.

Though several well-known projects, such as BOINC Collatz Conjecture run by volunteers all over the world, On 3x+1 Problem by Eric Roosendaal and Computational Verification of the 3x+1 Conjecture by Tomás Oliveira e Silva, have been testing the Collatz conjecture for many years for all numbers one by one from 0 to currently about 2^{72} or 10^{22}, we decided to test if large Mersenne primes are in agreement with Collatz conjecture.

Mersenne primes were selected for test since it is proven that if p is a power in N = 2^{p} – 1 (as is true for all Mersenne numbers), then the first 2p numbers in Collatz sequence will be above N.

In addition, the empirical results demonstrate that all path records for Collatz sequences are close to 2^{p }.

The first number that we test will be the 23rd Mersenne prime М11213 (or 2^{11213}-1, or about 2.81*10^{3375}).

This number is far beyond and by many orders of magnitude higher than any other number tested by mathematicians so far.

The test will be run with the use of our “3000 Collatz Tester” and its modifications.

We will report the results in due course.